Abstract
In this paper, we introduce the notion of C ´ iri c ´ type α - ψ - Θ -contraction and prove best proximity point results in the context of complete metric spaces. Moreover, we prove some best proximity point results in partially ordered complete metric spaces through our main results. As a consequence, we obtain some fixed point results for such contraction in complete metric and partially ordered complete metric spaces. Examples are given to illustrate the results obtained. Moreover, we present the existence of a positive definite solution of nonlinear matrix equation X = Q + ∑ i = 1 m A i * γ ( X ) A i and give a numerical example.
Highlights
Introduction and PreliminariesIn 1922, Polish mathematician Banach [1] proved an interesting result known as “Banach contraction principle" which led to the foundation of metric fixed point theory
The purpose of this paper is to define the notion of Ćirić type α-ψ-Θ-contraction and prove some best proximity point results in the frame work of complete metric spaces
As an application of results proven in above sections, we deduce new fixed point results for Ćirić type α-ψ-Θ-contraction in the frame work of metric and partially ordered metric spaces
Summary
In 1922, Polish mathematician Banach [1] proved an interesting result known as “Banach contraction principle" which led to the foundation of metric fixed point theory. His contribution gave a positive answer to the existence and uniqueness of the solution of problems concerned. N =1 and that F is α-admissible if for all x, y ∈ X α( x, y) ≥ 1 ⇒ α( Fx, Fy) ≥ 1, (1). Where α: X × X → [0, ∞) and proved some fixed point results for such mappings in the context of complete metric spaces (X, d). Symmetry 2019, 11, 93 of α-ψ-contractive, α-admissible mappings and proved certain fixed point results. In 2014, Jleli et al [4]
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